Table 2
Summary of the logarithmic slopes at the shell-crossing obtained by singularity theory applied to LPT predictions at various orders (see Appendix D for details).
| Sine wave amplitudes | Designation |  |
 |
 |
 |
 |
|---|---|---|---|---|---|---|
| 0 ≤ –ϵz ≤ –ϵy ≤ –ϵx | Q1D-2SIN, ANI-2SIN, Q1D-3SIN, ANI-3SIN | –2/3 | 2/3 | 2/3 | 1/3 | –5/3 |
| ϵz =0, 0 < –ϵy = –ϵx | SYM-2SIN | –4/3 | 2/3 | 2/3 | 1/3 | –7/3 |
| 0 < –ϵz=–ϵy =–ϵx | SYM-3SIN | –2 | 2/3 | 2/3 | 1/3 | –3 |
Notes. The first and second columns indicate the relative amplitudes of the initial sine waves and the designation of the runs, respectively. The third through seventh columns show the logarithmic slopes of the normalised density, velocity dispersion, radial velocity dispersion, infall velocity, and pseudo phase-space density, respectively. We thus note that the logarithmic slopes do not depend, as expected, on the perturbation order of LPT.
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